EDA for Consumer Staples Sector Fund

The Consumer Staples Sector Fund (XLP) is an exchange-traded fund (ETF) that provides investors with exposure to the consumer staples sector of the US economy. The fund holds a diverse range of companies, including those involved in food and beverage production, personal and household products, and tobacco. XLP is a popular choice for investors looking for stability and consistent dividends, as the companies within the sector tend to have steady earnings and demand regardless of economic conditions. Overall, XLP can be a valuable addition to a well-diversified portfolio, providing exposure to a resilient sector of the US economy.

Time Series Plot

Code

# get data
options("getSymbols.warning4.0"=FALSE)
options("getSymbols.yahoo.warning"=FALSE)


data = getSymbols("XLP",src='yahoo', from = '2010-01-01',to = "2023-03-01")

df <- data.frame(Date=index(XLP),coredata(XLP))

# create Bollinger Bands
bbands <- BBands(XLP[,c("XLP.High","XLP.Low","XLP.Close")])

# join and subset data
df <- subset(cbind(df, data.frame(bbands[,1:3])), Date >= "2010-01-01")

#export the data 
XLP_data <- df
write.csv(XLP_data, "DATA/CLEANED DATA/XLP_raw_data.csv", row.names=FALSE)

# colors column for increasing and decreasing
for (i in 1:length(df[,1])) {
  if (df$XLP.Close[i] >= df$XLP.Open[i]) {
      df$direction[i] = 'Increasing'
  } else {
      df$direction[i] = 'Decreasing'
  }
}

i <- list(line = list(color = '#2297E6'))
d <- list(line = list(color = '#7F7F7F'))

# plot candlestick chart

fig <- df %>% plot_ly(x = ~Date, type="candlestick",
          open = ~XLP.Open, close = ~XLP.Close,
          high = ~XLP.High, low = ~XLP.Low, name = "XLP",
          increasing = i, decreasing = d) 
fig <- fig %>% add_lines(x = ~Date, y = ~up , name = "B Bands",
            line = list(color = '#ccc', width = 0.5),
            legendgroup = "Bollinger Bands",
            hoverinfo = "none", inherit = F) 
fig <- fig %>% add_lines(x = ~Date, y = ~dn, name = "B Bands",
            line = list(color = '#ccc', width = 0.5),
            legendgroup = "Bollinger Bands", inherit = F,
            showlegend = FALSE, hoverinfo = "none") 
fig <- fig %>% add_lines(x = ~Date, y = ~mavg, name = "Mv Avg",
            line = list(color = '#E377C2', width = 0.5),
            hoverinfo = "none", inherit = F) 
fig <- fig %>% layout(yaxis = list(title = "Price"))

# plot volume bar chart
fig2 <- df 
fig2 <- fig2 %>% plot_ly(x=~Date, y=~XLP.Volume, type='bar', name = "XLP Volume",
          color = ~direction, colors = c('#2297E6','#7F7F7F')) 
fig2 <- fig2 %>% layout(yaxis = list(title = "Volume"))

# create rangeselector buttons
rs <- list(visible = TRUE, x = 0.5, y = -0.055,
           xanchor = 'center', yref = 'paper',
           font = list(size = 9),
           buttons = list(
             list(count=1,
                  label='RESET',
                  step='all'),
             list(count=3,
                  label='3 YR',
                  step='year',
                  stepmode='backward'),
             list(count=1,
                  label='1 YR',
                  step='year',
                  stepmode='backward'),
             list(count=1,
                  label='1 MO',
                  step='month',
                  stepmode='backward')
           ))

# subplot with shared x axis
fig <- subplot(fig, fig2, heights = c(0.7,0.2), nrows=2,
             shareX = TRUE, titleY = TRUE)
fig <- fig %>% layout(title = paste("Consumer Staples Sector Fund Stock Price: JAN 2010 - March 2023"),
         xaxis = list(rangeselector = rs),
         legend = list(orientation = 'h', x = 0.5, y = 1,
                       xanchor = 'center', yref = 'paper',
                       font = list(size = 10),
                       bgcolor = 'transparent'))

fig

Since its inception in 1998, the Consumer Staples Sector Fund (XLP) has experienced various trends and fluctuations over the years. In the period from 2010 to March 2023, XLP has seen several ups and downs due to various factors, including changes in the global economy, geopolitical events, and consumer behavior.

In the early part of the decade, XLP experienced a relatively stable period with consistent growth, as the economy began to recover from the financial crisis of 2008. However, in 2015 and 2016, XLP experienced a downturn, as the global economy slowed down, and there was increased volatility in the markets.

The fund saw a significant uptick in 2017, as investors sought safety in defensive stocks amid political and economic uncertainty. The fund’s performance remained relatively strong in 2018 and 2019, as consumer staples continued to outperform other sectors.

However, the COVID-19 pandemic in 2020 caused significant disruptions to the global economy, leading to a sharp decline in XLP in the first quarter. Still, the fund bounced back quickly, as consumer staples became a preferred investment for investors seeking safety during the pandemic.

In 2021, XLP’s performance remained relatively stable, with minor fluctuations due to inflation concerns and rising interest rates. Overall, XLP has proven to be a reliable investment option for investors looking for stability and consistent returns over the years.

For stock prices, a multiplicative decomposition is typically preferred because the percentage changes in stock prices tend to be more important than the absolute changes. Additionally, stock prices tend to exhibit non-constant variance, meaning that the variance of the series changes over time. A multiplicative decomposition can handle this non-constant variance more effectively than an additive decomposition.

Decomposed Time Series

Decomposition Plot

Code

#time series data
myts<-ts(df$XLP.Adjusted,frequency=252,start=c(2010,01,01), end = c(2023,3,1)) 
#original plot for time series data
orginial_plot <- autoplot(myts,xlab ="Year", ylab = "Adjusted Closing Price", main = "Consumer Staples Sector Fund Stock price: JAN 2010 - March 2023")
#decompose the data
decompose = decompose(myts, "multiplicative")
#decomposition plot
autoplot(decompose)

Adjusted Decomposition Plot

Code

#adjusted plot
trendadj <- myts/decompose$trend
decompose_adjtrend_plot <- autoplot(trendadj,ylab='trend') +ggtitle('Adjusted trend component in the multiplicative time series model')
seasonaladj <- myts/decompose$seasonal
decompose_adjseasonal_plot <- autoplot(seasonaladj,ylab='seasonal') +ggtitle('Adjusted seasonal component in the multiplicative time series model')
grid.arrange(orginial_plot, decompose_adjtrend_plot,decompose_adjseasonal_plot, nrow=3)

The adjusted seasonal component tend to have upward trend and there is more variability in the model when compared to the original plot where the variation during the years but the adjusted trend then to have more fluctuation showing no trend when compared to the original plot.

Lag Plots

Daily Time Lags

Code

#Lag plots 
gglagplot(myts, do.lines=FALSE, lags=1)+xlab("Lag 1")+ylab("Yi")+ggtitle("Lag Plot for Consumer Staples Sector Fund Stock JAN 2010 - March 2023")

Monthly Time Lags

Code

#montly data
mean_data <- df %>% 
  mutate(month = month(Date), year = year(Date)) %>% 
  group_by(year, month) %>% 
  summarize(mean_value = mean(XLP.Adjusted))
month<-ts(mean_data$mean_value,start = c(2010, 1),frequency = 12)
#Lag plot
ts_lags(month)

The first lag plot shows the daily time lags of the Consumer Staples Sector Fund stock price from JAN 2010 to March 2023. The plot indicates that there is a strong positive correlation between the current value and the previous day’s value, as seen by the points clustering along the diagonal line. This suggests that the stock price has a positive autocorrelation at a lag of one day.

The second lag plot shows the monthly time lags of the mean value of the Consumer Staples Sector Fund stock price from JAN 2010 to March 2023. The plot indicates that there is a positive correlation between the current value and the value from the previous month. This suggests that the mean value of the stock price has a positive autocorrelation at a lag of one month.

Overall, the lag plots indicate that there is a positive autocorrelation present in the Consumer Staples Sector Fund stock price data, with the strongest correlation observed in the daily time series.

Seasonality

Seasonal Heatmap

Code

# Create seasonal plot
ts_heatmap(month, color = "BuGn", title = 'Seasonality Heatmap of Consumer Staples Sector Fund Stock Jan 2010 - March 2023')

Seasonal Line plot

Code

# Create a line graph for each year with months on the x-axis
ggseasonplot(month, datecol = "date", valuecol = "value")+ggtitle("Seasonal Yearly Plot for Consumer Staples Sector Fund Stock Jan 2010 - March 2023")

The Seasonality Heatmap for the Consumer Staples Sector Fund Stock JAN 2010 - March 2023 does not reveal any clear seasonality in the data. The heatmap shows the mean value of the time series for each month and year combination, with the darker colors indicating higher values. The lack of clear patterns or darker colors in specific months or years suggests that there is no consistent seasonal pattern in the data. However, the yearly line graph shows a slight upward trend in the stock price from 2010 to 2023, but does not show any clear seasonality. Each year’s data is represented by a line, and the months are plotted on the x-axis. Overall, the lack of clear seasonality in both the heatmap and yearly line graph suggests that other factors beyond seasonality are driving the stock price fluctuations.

Moving Average

4 Month MA

Code

#SMA Smoothing 
ma <- autoplot(month, series="Data") +
  autolayer(ma(month,5), series="4 Month MA") +
  xlab("Year") + ylab("GWh") +
  ggtitle("Consumer Staples Sector Fund Stock JAN 2010 - March 2023(4 Month Moving Average)") +
  scale_colour_manual(values=c("Data"="grey50","4 Month MA"="red"),
                      breaks=c("Data","4 Month MA"))
ma

1 Year MA

Code

#SMA Smoothing 
ma <- autoplot(month, series="Data") +
  autolayer(ma(month,13), series="1 Year MA") +
  xlab("Year") + ylab("GWh") +
  ggtitle("Consumer Staples Sector Fund Stock JAN 2010 - March 2023(1 Year Moving Average)") +
  scale_colour_manual(values=c("Data"="grey50","1 Year MA"="red"),
                      breaks=c("Data","1 Year MA"))
ma

3 Year MA

Code

#SMA Smoothing 
ma <- autoplot(month, series="Data") +
  autolayer(ma(month,37), series="3 Year MA") +
  xlab("Year") + ylab("GWh") +
  ggtitle("Consumer Staples Sector Fund Stock JAN 2010 - March 2023(3 Year Moving Average)") +
  scale_colour_manual(values=c("Data"="grey50","3 Year MA"="red"),
                      breaks=c("Data","3 Year MA"))
ma

5 Year MA

Code

#SMA Smoothing 
ma <- autoplot(month, series="Data") +
  autolayer(ma(month,61), series="5 Year MA") +
  xlab("Year") + ylab("GWh") +
  ggtitle("Consumer Staples Sector Fund Stock JAN 2010 - March 2023(5 Year Moving Average)") +
  scale_colour_manual(values=c("Data"="grey50","5 Year MA"="red"),
                      breaks=c("Data","5 Year MA"))
ma

The four plots show the Consumer Staples Sector Fund stock prices from JAN 2010 to March 2023, along with the moving averages for 4 months, 1 year 3 years and 4 years. As the window of the moving average increases, the smoother the trend line becomes, reducing the impact of noise and fluctuations in the original time series.

The 4-month moving average plot shows frequent fluctuations in the stock price, with the trend line following the general direction of the time series. The 1-year moving average plot shows a smoother trend, following the overall upward trend of the stock price.

The 1-year moving average plot shows a similar trend to the 4-month plot but is even smoother, with fewer fluctuations. Finally, the 5-year moving average plot shows the smoothest trend, with an almost constant upward slope.As the moving average window increases, the smoother trend allows for a clearer identification of the general trend of the Consumer Staples Sector Fund stock prices over time. From the moving average obtained above we can see that there is upward tend in the stock price of Consumer Staples Sector Fund.

Autocorrelation Time Series

ACF

Code

#ACF for  data
ggAcf(month)+ggtitle("ACF Plot for Consumer Staples Sector Fund Stock JAN 2010 - March 2023")

PACF

Code

#PACF for data
ggPacf(month)+ggtitle("PACF Plot for Consumer Staples Sector Fund Stock JAN 2010 - March 2023")

ADF Test

Code

#check the stationarity
tseries::adf.test(month)

    Augmented Dickey-Fuller Test

data:  month
Dickey-Fuller = -2.0836, Lag order = 5, p-value = 0.5415
alternative hypothesis: stationary

In the plot of autocorrelation function, which is the acf graph for monthly data, there are clear autocorrelation in lag. The above lag plots and autocorrelation plot indicates seasonality in the series, which means the series is not stationary. It was also verified using Augmented Dickey-Fuller Test which tells us that as the p value is greater than 0.05, the series is not stationary.

Detrend and Differenced Time Series

Linear Fitting Model

Code

fit = lm(myts~time(myts), na.action=NULL) 
summary(fit) 

Call:
lm(formula = myts ~ time(myts), na.action = NULL)

Residuals:
     Min       1Q   Median       3Q      Max 
-13.5256  -1.0564   0.2343   1.3352  10.7104 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -8.255e+03  2.630e+01  -313.9   <2e-16 ***
time(myts)   4.115e+00  1.304e-02   315.5   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.805 on 3277 degrees of freedom
Multiple R-squared:  0.9681,    Adjusted R-squared:  0.9681 
F-statistic: 9.953e+04 on 1 and 3277 DF,  p-value: < 2.2e-16

ACF Plot

Code

# plot ACFs
plot1 <- ggAcf(myts, 48, main="Original Data: Consumer Staples Sector Fund Stock Stock Price")
plot2 <- ggAcf(resid(fit), 48, main="Detrended data")
plot3 <- ggAcf(diff(myts), 48, main="First differenced data")
grid.arrange(plot1, plot2, plot3, nrow=3)

The estimated slope coefficient β1, 0.7645 With a standard error of 0.0597, yielding a significant estimated increase of stock price is very less yearly. Equation of the fit for stationary process: \[\hat{y}_{t} = x_{t}+(1502.6506)-(0.7645)t\]

From the above graph we can say that there is no change in detrended plot and the original data acf plot, it typically means that the data is stationary. But when the first order difference is applied the high correlation is removed but there is no seasonal correlation.

As depicted in the above figure, the series is now stationary and ready for future study.